The present invention generally pertains to electronic communications and is particularly directed to improving image rejection in a system for converting an analog signal into (I) in-phase and a (Q) quadrature-phase digital signals for digital signal processing.
A common prior art method of converting a received analog signal for digital processing is to split the received analog signal into an in-phase (I) component and a quadrature-phase (Q) component and to separately convert these two components into digital signals. A typical prior art system for accomplishing such conversion is described with reference to FIG. 1. This prior art system includes a first mixer 10, a second mixer 12, a phase shifter 14, a frequency generator 16, a first filter 18, a second filter 20, a first amplifier 22, a second amplifier 24, a first A/D converter 26 and a second A/D converter 28. This system converts a high frequency analog input signal A.multidot.sin ((.omega..sub.o +.omega..sub.s)t+.phi.)) received at terminal 30 into baseband signals A.multidot.M.multidot.sin (.omega..sub.s t+.phi.) on line 32 to provide the I component, and A.multidot.N.multidot.cos (.omega..sub.s t+.phi.) on line 34 to provide the Q component.
.omega..sub.s is the baseband frequency. PA0 .omega..sub.o is the IF center frequency. PA0 .phi. is phase of the input signal. PA0 M is the gain of the I channel 10, 18, 22. PA0 N is the gain of the Q channel 12, 20, 24.
The I and Q components on lines 32 and 34 are repeatedly sampled by the respective A/D converters 26 and 28 simultaneously in response to a clock signal on line 36 to provide an I digital signal at output terminal 38 and a Q digital signal at output terminal 40. The obtained binary values for the I and Q digital signals represent the baseband signal vector at the instant of sampling, and repeated sampling by A/D conversion provides an accurate representation of the baseband components on lines 32 and 24, including the information contained in the modulation of the input signal. There is no restriction on the kind of modulation, such as AM, FM, PM, BPSK, QPSK, etc.
The accuracy of this conversion is limited in practical applications due to unavoidable I/Q gain imbalance (i.e. N/M not being equal to 1 and phase errors (e.sub..phi.) due to the I and Q signals not being offset by exactly ninety degrees from each other. These errors cause generation of a baseband image signal at -.omega..sub.s (where .omega..sub.s is the baseband signal frequency). Although the image signal is at a lower level than the baseband signals, the level is too high for many applications. For the image signal produced in the prior art system of FIG. 1, the image rejection (IR) with respect to the baseband signal is: ##EQU2##
For typical achievable imbalances of ##EQU3## and a phase error of e.sub..phi. =3 degrees, the image rejection is 24 dB.
Another prior art method of converting an analog input signal for digital processing is to bandpass sample the analog input signal A.multidot.sin ((.omega..sub.o +.omega..sub.s)t+.phi.)) at a sampling rate of f=1/.tau. to provide a sequence of digital signal samples: EQU S.sub.0 =A.multidot.sin .phi., EQU S.sub.1 =A.multidot.cos (.omega..sub.s .tau.+.phi.), EQU S.sub.2 =-A.multidot.sin (.omega..sub.s .multidot.2.tau.+.phi.), EQU S.sub.3 =-A.multidot.cos (.omega..sub.s .multidot.3.tau.+.phi.), EQU S.sub.4 =A.multidot.sin (.omega..sub.s .multidot.4.tau.+.phi.), EQU S.sub.5 =A.multidot.cos (.omega..sub.s .multidot.5.tau.+.phi.), EQU S.sub.6 =-A.multidot.sin (.omega..sub.s .multidot.6.tau.+.phi.), . . . ;
wherein .omega..sub.s is the baseband frequency, .omega..sub.o is the IF center frequency, and .phi. is the phase of the input signal. These digital signal samples are processed to provide a sequence of in-phase digital signals, I.sub.1, I.sub.2, I.sub.3 and a sequence of quadrature-phase digital signals, Q.sub.1, Q.sub.2, Q.sub.3.
Advantages of the bandpass sampling technique are that only one A/D converter is required and that there is no balance or tracking requirements for the different parts of the circuitry.
The choices of the sampling frequencies f are:
f=4 f.sub.o /(4 m+2 a-1), wherein m is 0, 1, 2, . . . ; and a is either 0 or 1. This provides samples that are 90 degrees apart for the IF center frequency .omega..sub.o. However, frequencies that are offset from the IF center frequency have a phase error e.sub..phi.) equal to .omega..sub.s .tau.. With .omega..sub.s .tau.=the baseband frequency=the offset frequency, the rejection is a function of the baseband frequency .omega..sub.s, and thereby becomes: ##EQU4##
Although this is equivalent to the I/Q split model of FIG. 1, with no gain imbalance, (i.e. N/M=1) and the phase error, e.sub..phi. =.omega..tau., this prior art bandpass sampling technique provides a significant improvement over the prior art system of FIG. 1 by almost doubling the dB value of the image rejection.
For an UHF receiver with 25 KHz wide channels, the maximum baseband frequency is 12.5 KHz. When sampled at f=4 MHz, the image rejection is 40 dB.
For some demanding applications, however, the image rejection must be much greater.